A Novel and Simple Mathematical Transform Improves the Perfomance of Lernmatrix in Pattern Classification

José-Luis Velázquez-Rodríguez, Yenny Villuendas-Rey, Oscar Camacho-Nieto and Cornelio Yáñez-Márquez
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José-Luis Velázquez-Rodríguez: Centro de Investigación en Computación, Instituto Politécnico Nacional, CDMX 07738, Mexico
Yenny Villuendas-Rey: Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, CDMX 07700, Mexico
Oscar Camacho-Nieto: Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, CDMX 07700, Mexico
Cornelio Yáñez-Márquez: Centro de Investigación en Computación, Instituto Politécnico Nacional, CDMX 07738, Mexico

Mathematics, 2020, vol. 8, issue 5, 1-46

Abstract: The Lernmatrix is a classic associative memory model. The Lernmatrix is capable of executing the pattern classification task, but its performance is not competitive when compared to state-of-the-art classifiers. The main contribution of this paper consists of the proposal of a simple mathematical transform, whose application eliminates the subtractive alterations between patterns. As a consequence, the Lernmatrix performance is significantly improved. To perform the experiments, we selected 20 datasets that are challenging for any classifier, as they exhibit class imbalance. The effectiveness of our proposal was compared against seven supervised classifiers of the most important approaches (Bayes, nearest neighbors, decision trees, logistic function, support vector machines, and neural networks). By choosing balanced accuracy as a performance measure, our proposal obtained the best results in 10 datasets. The elimination of subtractive alterations makes the new model competitive against the best classifiers, and sometimes beats them. After applying the Friedman test and the Holm post hoc test, we can conclude that within a 95% confidence, our proposal competes successfully with the most effective classifiers of the state of the art.

Keywords: associative memories; Lernmatrix; pattern classification; mathematical transform; Johnson-Möbius code (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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